Nakayama自同构和滤形变下的模导子之间的关系
2024.10.18
投稿：龚惠英部门：理学院浏览次数：
活动信息
报告题目 (Title)：Relation between the Nakayama automorphisms and modular derivations under filtered deformations（Nakayama自同构和滤形变下的模导子之间的关系）
报告人 (Speaker)：吴泉水 教授（复旦大学）
报告时间 (Time)：2024年10月22日(周二) 16:10-17:10
报告地点 (Place)： 校本部D109
邀请人(Inviter)：毛雪峰、黄红娣
主办部门： 理学院数学系
报告摘要：对于任何positively flitered代数，通常斜Calabi-Yau性质和Van den Bergh对偶可以提升，但Calabi-Yau性质则不能。Calabi-Yau性质通常源自unimodular泊松结构的微扰。假设A是一个具有交换Calabi-Yau相关分次代数gr(A)的滤代数。则gr(A)是一具有modular导子的典范泊松结构。我们将同调行列式作为桥梁来描述A的Nakayama自同构与gr(A)的modular导子之间的联系。特别是，在某些温和的假设下，我们证明了A是Calabi-Yau代数当且仅当gr(A)作为泊松代数是unimodular的。作为应用我们证明：一个光滑代数簇上的微分算子环是Calabi-Yau代数。我们还将在报告中介绍其他的应用.
Abstract：
For any positively filtered algebra, the property of skew Calabi-Yau or having Van den Bergh duality can be lifted as usual, but not for Calabi-Yau property. Calabi-Yau property often emerges form the deformation of unimodular Poisson structure. Suppose A is a filtered algebra such that the associated graded algebra gr(A) is commutative Calabi-Yau. Then gr(A) has a canonical Poisson structure with a modular derivation. We describe the connection between the Nakayama automorphism of A and the modular derivation of gr(A) by using homological determinants as a bridge. In particular, it is proved that A is Calabi-Yau if and only if gr(A) is unimodular as Poisson algebra under some mild assumptions. As an application, we derive that the ring of differential operators over a smooth variety is Calabi-Yau. Some other applications will also be given in the talk.
